The analysis of action of the account imperfection is conducted during investigations of deformable body's behavior based on geometrical linear and nonlinear mathematical models. The linearity of boundary conditions set in strain on real (indignant) body boundary at deformable state is realized. During investigation of elastic strengthened plate's strain-deformable state the condition by execution of which small parameters rows are coincided with Taylor's rows is found. The problem solution described the behavior of compressed elastic strengthened plate is found with a exactness to fist order small values 

In the note is proved that Hardy tarnsformation T: (Tf)(z)=Σk<1(a0+...+ak) zk/k, f(z)=Σk>0ak zk, where f is a holomorphic in the unit disk function, is acting continuously in Bergman Apα and Hardy Hp spaces with 0<p<1 

В работе приведены новые волновые уравнения, описывающие нелинейную динамику импульсов, которые состоят всего из нескольких колебаний светового поля, в прозрачных оптических средах. Рассмотрен ряд явлений оптики таких предельно коротких импульсов: формирование предельно коротких солитонов, генерация спектрального суперконтинуума и возможность сжатия его в импульс, состоящий лишь из одной полной осцилляции светового поля, образование предельно коротких ударных волн, формирование фемтосекундных "световых игл" и другие 

The phenomenon of ultrabroadening of spectra of intensive femtosecond laser pulses in transparent isotropic media with instant electron and inertial electron-vibrational nonlinearities is studied on the basis of numerical solutions of new nonlinear wave equations for pulse elictrical field. The results of numerical simulations of spectral supercontinuum evolution by propagation of several light field oscillations pulses in fused silica are given. It is shown that because of inertia of electron-vibrational nonlinearity in fused silica spectral supercontinuum develops slower than in media with instant nonlinearity. The conditions of optimal time compressing of femtosecond pulses with continuum spectrum are made more accurate 

The effects of light pulses with a few field oscillations polarizing selfaction are studied on the basis of numerical modeling of new nonlinear wave equations for pulse electric field. The results of numerical simulations of several light field oscillations pulses with any polarization in fused silica and argon are given. It is shown that polarizing selfaction consists of nonuniform rotation of polarizing ellipse, and spectra ultrabroadening of pulses with any polarization develops slower than for linearly polarized pulses 

This work is about a fundamental question of relationship between external, local, and averaged electrostatic field in nonpolar anisotropic dielectrics. The interdependence between the last two vectors gives the dielectric permittivity of the artificial dielectric under consideration. This work contains the exact deduction of the Clausius-Mossotti and Lorentz-Lorenz formulae for the regular lattice with parallelepipedal elementary cell of inclusions with smooth surface. We pay the special attention to the concept of dyadic interaction constant (factor of locality). An artificial dielectric is under consideration. It makes possible to be restricted to classical electrostatics without additional approximations. The numerical calculation results for dyadic interaction constant for oblique-angled lattices are given 

Electromagnetic excitation of regular arrays of bianisotropic particles by plane waves is considered. Arrays (grids) are assumed to be infinite and the particles to be small compared to the wavelength, so that the dipole approximation is possible. The elecromagnetic interaction between all the particles is taken into account analytically. The analytical model under consideration allows to express the electric and magnetic moments induced in each particle through incident wave fields amplitudes in terms of excitation dyadics. Two kinds of bianisotropic particles: chiral particles and omega particles are analyzed in this work. One- (linear array), two- (planar array) and three-dmensional (multilayered) arrays are considered, and for all of them analytical expression for key and excitation dyadics presented. Also the numerical calculation based on the formulae that have been developed is presented 

Modes of reflected and passed waves emission in the induced superradiation are studied. The case of continuous reduction of inversion at the sample end faces is considered. It is shown that the size of domain of the inversion smoothing essentially effects a ratio of direct and opposite waves 

The physical modeling of different types of magnetic anisotropy of rocks has been carried out. The investigation of magnetic anisotropy of model samples and samples of igneous rocks by magnetic torque method showed that the existing torque curves interpretation technique using phases values of their second harmonics is not acceptable for the case of multicomponent anisotropy of rocks since it doesn't allow us to subdivide magnetic anisotropy into uniaxial components. New interpretation technique based on spherical harmonic analysis has been developed. Application of this technique for the interpretation of torque curves of model samples shows that it gives a possibility of subdivision of magnetic anisotropy into uniaxial physical components 

Thermal and saline state of stratified water masses of the World Ocean is described by means of probabilistic model of inhomogeneous Gaussian random function for vertical distribution of steady state thermodynamic parameters. On the base of this model the statistical criterion for quality control is proposed for temperature and salinity oceanographic data on the standard depths